The equilibrium constant for the reactions
` N_2(g) +O_2(g) hArr 2NO ( g)`
is ` 4xx 10 ^(-4)` at 2000 K . In the presence of a catalyst. The equilibrium is attained three times faster. The equilibrium constant in the presence of the catalyst at 2000 K is

Options

A. ` 40xx 10 ^(-4)`
B. ` 4 xx 10 ^(-4)`
C. ` 1.2 xx 10 ^(-3)`
D. difficult to compute without more data.

Answer

To solve the problem, we need to understand the role of a catalyst in a chemical reaction and its effect on the equilibrium constant.

### Step-by-Step Solution

1. **Identify the Given Information**:
- The reaction is:
\[ N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \]
- The equilibrium constant (\(K\)) at 2000 K is given as:
\[ K = 4 \times 10^{-4} \]
- A catalyst is present, and it is stated that the equilibrium is attained three times faster.

2. **Understand the Effect of a Catalyst**:
- A catalyst increases the rate of a reaction but does not change the equilibrium constant. It helps the system reach equilibrium faster but does not alter the position of equilibrium or the value of \(K\).

3. **Conclusion**:
- Since the equilibrium constant is not affected by the presence of a catalyst, the equilibrium constant at 2000 K remains:
\[ K = 4 \times 10^{-4} \]

4. **Final Answer**:
- The equilibrium constant in the presence of the catalyst at 2000 K is:
\[ \boxed{4 \times 10^{-4}} \]